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Abstract

this article, we review some of the characteristic features of ad hoc networks, formulate problems and survey research work done in the area. We focus on two basic problem domains: topology control, the problem of computing and maintaining a connected topology among the network nodes, and routing. This article is not intended to be a comprehensive survey on ad hoc networking. The choice of the problems discussed in this article are somewhat biased by the research interests of the author

Citations

...se due to network changes, clusterings based on a small number of clusters are desirable. The problem ofsnding a dominating set of minimum size, however, is a classic NP-complete optimization problem =-=[18]-=- and it is known that unless NP has n O(log log n) -time deterministic algorithms, the best approximation ratio achievable in polynomial time is O(log n) [15]. In the context of ad hoc networks, we ar...

...frequent changes in the system and completely decentralized organization. An interesting direction for future research is to see whether resource location protocols designed for peer-to-peer networks =-=[28, 39, 42, 48-=-] can be adapted to yield eective routing protocols for ad hoc networks. Finally, we note that most of the results we have discussed in this article rely on MAC layer protocols for power control and c...

...frequent changes in the system and completely decentralized organization. An interesting direction for future research is to see whether resource location protocols designed for peer-to-peer networks =-=[28, 39, 42, 48-=-] can be adapted to yield eective routing protocols for ad hoc networks. Finally, we note that most of the results we have discussed in this article rely on MAC layer protocols for power control and c...

.... While the idea of aggressive caching and occasional update results in good average performance, the worst-case latency could be high. Examples of reactive protocols are Dynamic Source Routing (DSR) =-=[25]-=-, Ad-hoc OnDemand Distance Vector Routing (AODV) [36], and TORA [35]. For a comparison of certain proactive and reactive routing protocols, see [13]. Hybrids of proactive and reactive protocols, e.g.,...

...to designing simple protocols that keep overhead small is to exploit the underlying geometry (and geography) of the ad hoc network locations. In the Greedy Perimeter Stateless Routing (GPSR) protocol =-=[27], eac-=-h node only maintains information about their \neighborhood&quot;, which is the set of nodes that the node can directly reach. Using positioning information, the source node greedily passes a given pa...

...space (clear, unobstructed line-of-sight path), we have PR = O P t d : (1) The hidden constant in the big-Oh notation in Equation 1 depends on antenna gains and the carrier frequency, and = 2 [41,=-= 50-=-]. We also note that the particular values of the hidden constants also depend on the units used for expressing the dierent parameters (such as PR , P t and d). Realistic environments are not free-spa...

... in good average performance, the worst-case latency could be high. Examples of reactive protocols are Dynamic Source Routing (DSR) [25], Ad-hoc OnDemand Distance Vector Routing (AODV) [36], and TORA =-=[35]-=-. For a comparison of certain proactive and reactive routing protocols, see [13]. Hybrids of proactive and reactive protocols, e.g., Zone Routing Protocol [22], have also been proposed, that maintain ...

... classic NP-complete optimization problem [18] and it is known that unless NP has n O(log log n) -time deterministic algorithms, the best approximation ratio achievable in polynomial time is O(log n) =-=[15-=-]. In the context of ad hoc networks, we are interested in distributed algorithms forsnding a small dominating set. Kutten and Peleg describe a distributed dominating set algorithm which takes O(log ...

...ting from traditional network design is that we need to determine the topology in a completely distributed environment. A number of distributed topology control algorithms have been proposed recently =-=[32, 43, 52, 53-=-]. These algorithms draw upon computational geometry techniques that dene connected topologies on points in Euclidean space. The techniques, and the topologies obtained, vary in the degree of simplici...

...frequent changes in the system and completely decentralized organization. An interesting direction for future research is to see whether resource location protocols designed for peer-to-peer networks =-=[28, 39, 42, 48-=-] can be adapted to yield eective routing protocols for ad hoc networks. Finally, we note that most of the results we have discussed in this article rely on MAC layer protocols for power control and c...

...nce Vector Routing (AODV) [36], and TORA [35]. For a comparison of certain proactive and reactive routing protocols, see [13]. Hybrids of proactive and reactive protocols, e.g., Zone Routing Protocol =-=[22]-=-, have also been proposed, that maintain a clustering of the network and keep routing information up-to-date within a cluster while using a reactive paradigm for collecting information about distant n...

...o energy-eciency, GG has energy-stretch of 1 and hence is optimal, while RNG has polynomial energy-stretch. The worst-case degree of GG issn). An elegant generalization of proximity graphs due to Yao =-=[56]-=- yields spanners for an arbitrary collection of points insnite-dimensional Euclidean space. Given a set of nodes in 2-dimensional space, suppose we partition the space around each node into sectors of...

...s with low load; the load on a node is signied by the height of the buer [8]. (The local balancing approach has also formed the basis of fast algorithms for load balancing [3] and multicommoditysow [9=-=].) For -=-a given T B + 2( 1), the algorithm of [8] is O(1 &quot;; 1 + (1 + (T + )=B)L=&quot;)-competitive, where L is the average path length used by successful packets in an optimal solution; in particular, ...

...rotocol by considering the amount of work needed to be done when an elementary change in the transmission graph occurs; that is, when an edge is removed or added or the neighborhood of a node changes =-=[17, 47]-=-. Another interesting model for capturing node mobility is the recently proposed adversarial network model [7], in which an adversary may alter the underlying graph in an unpredictable manner. Arbitra...

...ting from traditional network design is that we need to determine the topology in a completely distributed environment. A number of distributed topology control algorithms have been proposed recently =-=[32, 43, 52, 53-=-]. These algorithms draw upon computational geometry techniques that dene connected topologies on points in Euclidean space. The techniques, and the topologies obtained, vary in the degree of simplici...

...space (clear, unobstructed line-of-sight path), we have PR = O P t d : (1) The hidden constant in the big-Oh notation in Equation 1 depends on antenna gains and the carrier frequency, and = 2 [41,=-= 50-=-]. We also note that the particular values of the hidden constants also depend on the units used for expressing the dierent parameters (such as PR , P t and d). Realistic environments are not free-spa...

...inear in the number of nodes; the maximum degree of a node may besn) in the worst case, however. For a comprehensive survey on geometric spanners and other structures in geometric network design, see =-=[14-=-]. The spanner property only ensures the existence of distance- and energy-ecient paths; how are these paths computed online when routing requests arise? While for some topologies such as the -graph a...

...used on unicast energy usage. Also of interest is to identify energy-ecient structures for broadcast and multicast operations. A number of greedy heuristics for broadcast routing have been studied in =-=[51, 54]-=-. While it has been shown that a constant-factor approximation is achievable (in, fact, the minimum spanning tree is shown to be O(1)- approximate), the complexity of the optimization problem is still...

...m for calculating these paths in a distributed manner is not known. 4.4 Adversarial model A second framework for analyzing ad hoc network routing algorithms is the adversarial model,srst developed in =-=[12]-=- and subsequently enhanced in several recent studies [4, 8]. In the context of ad hoc networks, we can model mobility and trac patterns using an adversary. Mobility can be modeled by allowing the adve...

...not known. 4.4 Adversarial model A second framework for analyzing ad hoc network routing algorithms is the adversarial model,srst developed in [12] and subsequently enhanced in several recent studies =-=[4, 8]-=-. In the context of ad hoc networks, we can model mobility and trac patterns using an adversary. Mobility can be modeled by allowing the adversary to activate/deactivate network edges; arbitrary trac ...

...ich the distributed greedy algorithm takessn) time. Building upon NC algorithms for the set cover problem [11, 40], a randomized distributed implementation of the sequential algorithm is presented in =-=[24]-=- and is shown to achieve an O(log n) approximation in O(log 2 n) time with high probability. It is still open whether one can derive the same approximation in O(log n) time. Also, better approximation...

...nterference. In practice, power control and interference are usually addressed at the multiple-access layer of the OSI 7-layer hierarchy (e.g., the IEEE 802.11 MAC protocol and suggested enhancements =-=[2]-=-). Many routing protocols for ad hoc network separate the multiple-access control (MAC) and the network layer concerns. Thus, at the network layer, one can simply model the network as a directed graph...

...ves the direction and speed of the node. Each node independently chooses a mobility vector that denes its motion for a period of time, after which a new random mobility vector is assigned (e.g., see [=-=30, 33]-=-). Models for group movement, whereby a group of nodes may move in the same general direction have also been recently studied [2, 30]. For a theoretical analysis, detailed models of mobility, as above...

...ves the direction and speed of the node. Each node independently chooses a mobility vector that denes its motion for a period of time, after which a new random mobility vector is assigned (e.g., see [=-=30, 33]-=-). Models for group movement, whereby a group of nodes may move in the same general direction have also been recently studied [2, 30]. For a theoretical analysis, detailed models of mobility, as above...

...layers The radio propagation and interference models of Section 2.1 can be used to derive meaningful bounds on the capacity of ad hoc networks, given node locations and transmission power constraints =-=[20, 21]-=-. Such a model based on physical layer parameters, however, is cumbersome to use for designing and analyzing higher layer protocols. A simpler model that abstracts away the physical layer details is t...

...t network decomposition technique of sparse neighborhood covers to achieve a stretch of O(k 2 ) while using O(kn 1=k log 2 n log D) local memory overhead, where D is the diameter of the network. (See =-=[1-=-9] for a recent survey on tradeos in routing forsxed-connection networks.) Thus, the preced9 ing protocol guarantees the near-optimal tradeo of achieving O(polylog(n)) stretch while only using O(polyl...

...the nearest neighbor in each sector. If each sector has an angle of s=3, the resultant graph, commonly referred to as a -graph, has been shown to be a connected graph with stretch 1=(1 2 sin(=2)) [44]; thus, the -graph is a spanner. For ad hoc wireless networks, the -graph can be easily constructed using a fast local algorithm in which each node queries nodes within its transmission radius, and ...

...urs; that is, when an edge is removed or added or the neighborhood of a node changes [17, 47]. Another interesting model for capturing node mobility is the recently proposed adversarial network model =-=[7]-=-, in which an adversary may alter the underlying graph in an unpredictable manner. Arbitrary node movements can be represented by adversarial changes in topology. We discuss this model in greater deta...

...des with high load to nodes with low load; the load on a node is signied by the height of the buer [8]. (The local balancing approach has also formed the basis of fast algorithms for load balancing [3=-=] and mu-=-lticommoditysow [9].) For a given T B + 2( 1), the algorithm of [8] is O(1 &quot;; 1 + (1 + (T + )=B)L=&quot;)-competitive, where L is the average path length used by successful packets in an optimal...

...ting from traditional network design is that we need to determine the topology in a completely distributed environment. A number of distributed topology control algorithms have been proposed recently =-=[32, 43, 52, 53-=-]. These algorithms draw upon computational geometry techniques that dene connected topologies on points in Euclidean space. The techniques, and the topologies obtained, vary in the degree of simplici...

...ves the same approximation ratio as the greedy algorithm; however, there exist networks for which the distributed greedy algorithm takessn) time. Building upon NC algorithms for the set cover problem =-=[11, 40]-=-, a randomized distributed implementation of the sequential algorithm is presented in [24] and is shown to achieve an O(log n) approximation in O(log 2 n) time with high probability. It is still open ...

...tors, the level of interference inherent to the topology. Dene the interference number of an edge e in T to be the maximum number of other edges in T that interfere with e, in the sense of Section 2 [=-=6-=-]. Dene the interference number of the topology to be the maximum interference number of an edge in T . A plausible goal then is to seek a topology with a small interference number. The particular int...

...ves the same approximation ratio as the greedy algorithm; however, there exist networks for which the distributed greedy algorithm takessn) time. Building upon NC algorithms for the set cover problem =-=[11, 40]-=-, a randomized distributed implementation of the sequential algorithm is presented in [24] and is shown to achieve an O(log n) approximation in O(log 2 n) time with high probability. It is still open ...

...io of d(Xk, Y) and d(Xi, Y) [21, 31]. In another variant of Equation 3, it is assumed that the transmission by a node Xi with power P/ blocks all nodes that are reachable from Xi with power (1 + A)Pi =-=[1]-=-. 2.2 Modeling at higher layers The radio propagation and interference models of Section 2.1 can be used to derive meaningful bounds on the capacity of ad hoc networks, given node locations and transm...

... context of ad hoc networks, we are interested in distributed algorithms forsnding a small dominating set. Kutten and Peleg describe a distributed dominating set algorithm which takes O(log n) time [=-=29]-=- on any network, assuming a synchronous model of computation, in which each node can exchange a message with each neighbor in each step. The primary emphasis in [29] is on time complexity, however, an...

...of one-level clustering, as discussed in Section 4.1, can be easily generalized to a multilevel hierarchical network decomposition. Indeed, this is an old concept in networking dating back to the 70s =-=[26, 34-=-]. While many of the hierarchical routing protocols were originally designed forsxed networks, they are applicable, with suitable modication, for ad hoc networks. The main idea of hierarchical routing...

...edges in order by length and adding an edge (u; v) to the subgraph if there is no other edge (u; w) or (v; w) already added and having an angle close to that of (u; v) [45] (a related idea is used in =-=[5-=-]). The topology control algorithm of [53] adopts a similar approach to convert a -graph to a constant-degree spanner. The basic idea is to eliminate an edge between u and v if there exists a node w s...

... network of warsghters and their mobile platforms in battleelds. Indeed, a wealth of early research in the area involved the development of packet-radio networks (PRNs) and survivable radio networks [=-=16]-=-. While military applications still dominate the research needs in ad hoc networking, the recent rapid advent of mobile telephony and plethora of personal digital assistants has brought to the fore a ...

... stretch and O(1) memory overhead; the memory overhead is constant since each node needs to store the coordinates of the nearest node in each of a constant number of sectors. This approach is used in =-=[23]-=- for routing in the plane. The worst-case adaptability of the routing scheme is at least the maximum in-degree of a O-graph, which may be large; consequently, the movement of a single node may require...

... by A assuming the buer of each node is of size at most B 0 . We call A (c; s)-competitive if for all and B, we have A sB () c OPTB () r; for some value r 0 that is independent of OPTB () [8, 46]. The best result known for the above adversarial model is a simple local balancing algorithm that send packets from nodes with high load to nodes with low load; the load on a node is signied by the ...

...mber of potential commercial applications of ad hoc networks. Examples are disaster relief, conferencing, home networking, sensor networks, personal area networks, and embedded computing applications =-=[37]-=-. The lack of asxed infrastructure in ad hoc networks implies that any computation on the network needs to be carried out in a decentralized manner. Thus, many of the important problems in ad hoc netw...

...rotocol by considering the amount of work needed to be done when an elementary change in the transmission graph occurs; that is, when an edge is removed or added or the neighborhood of a node changes =-=[17, 47]-=-. Another interesting model for capturing node mobility is the recently proposed adversarial network model [7], in which an adversary may alter the underlying graph in an unpredictable manner. Arbitra...

...rotocols proposed for ad hoc networks. Most of these protocols rely on heuristics and, as such, do not provide provable worst-case guarantees. From a theoretical standpoint, the protocol presented in =-=[10-=-] provides a suitable tradeo between stretch and memory overhead. The routing protocol, designed forsxed-connection networks, uses the elegant network decomposition technique of sparse neighborhood co...

...ting from traditional network design is that we need to determine the topology in a completely distributed environment. A number of distributed topology control algorithms have been proposed recently =-=[32, 43, 52, 53-=-]. These algorithms draw upon computational geometry techniques that dene connected topologies on points in Euclidean space. The techniques, and the topologies obtained, vary in the degree of simplici...

...used on unicast energy usage. Also of interest is to identify energy-ecient structures for broadcast and multicast operations. A number of greedy heuristics for broadcast routing have been studied in =-=[51, 54]-=-. While it has been shown that a constant-factor approximation is achievable (in, fact, the minimum spanning tree is shown to be O(1)- approximate), the complexity of the optimization problem is still...

...k ; Y ) and d(X i ; Y ) [21, 31]. In another variant of Equation 3, it is assumed that the transmission by a node X i with power P i blocks all nodes that are reachable from X i with power (1 + )P i [=-=1]-=-. 2.2 Modeling at higher layers The radio propagation and interference models of Section 2.1 can be used to derive meaningful bounds on the capacity of ad hoc networks, given node locations and transm...